From 3f385e49fca33917bfcf5f6d61828bdd97c4468a Mon Sep 17 00:00:00 2001
From: sTertooy <5571903+sTertooy@users.noreply.github.com>
Date: Sat, 15 May 2021 18:25:25 +0200
Subject: [PATCH] Fix IsNormal, uprank FittingSubgroup method(#61)

Our IsNormal method was buggy (it incorrectly used `Pcp(H,U)`. After fixing this it is mostly equivalent to GAP's default method; so we remove ours and use the default.

This in turn revealed that our `FittingSubgroup` method may not be invoked for finite pcp groups, depending on which packages are loaded. Fix that by increasing its rank.
---
 gap/basic/pcpgrps.gi  | 16 ----------------
 gap/pcpgrp/fitting.gi |  2 +-
 tst/bugfix.tst        | 15 +++++++++++++++
 3 files changed, 16 insertions(+), 17 deletions(-)

diff --git a/gap/basic/pcpgrps.gi b/gap/basic/pcpgrps.gi
index 299aaa4..2f8f65a 100644
--- a/gap/basic/pcpgrps.gi
+++ b/gap/basic/pcpgrps.gi
@@ -158,22 +158,6 @@ function( H, U )
     return ForAll( GeneratorsOfGroup(U), x -> x in H );
 end );
 
-#############################################################################
-##
-#M IsNormal( H, U ) . . . . . . . . . . . . . . .test if U is normalized by H
-##
-InstallMethod( IsNormalOp, "for pcp groups",
-               IsIdenticalObj, [ IsPcpGroup, IsPcpGroup ],
-function( H, U )
-    local u, h;
-    for h in GeneratorsOfPcp( Pcp(H, U)) do
-        for u in Igs(U) do
-            if not u^h in U then return false; fi;
-        od;
-    od;
-    return true;
-end );
-
 #############################################################################
 ##
 #M Size( <pcpgrp> )
diff --git a/gap/pcpgrp/fitting.gi b/gap/pcpgrp/fitting.gi
index 1c75fe4..924d74e 100644
--- a/gap/pcpgrp/fitting.gi
+++ b/gap/pcpgrp/fitting.gi
@@ -56,6 +56,7 @@ end );
 ##
 InstallMethod( FittingSubgroup,
                "for pcp groups", [IsPcpGroup],
+			   SUM_FLAGS, # Prevent generic GAP library method for finite groups being ranked higher
 function( G )
     local efas, pcps, l, F, i;
 
@@ -253,4 +254,3 @@ InstallGlobalFunction( NilpotentByAbelianByFiniteSeries, function( G )
     if IndexNC( G, A ) = infinity then Error("wrong subgroup"); fi;
     return [G, A, F, U];
 end );
-
diff --git a/tst/bugfix.tst b/tst/bugfix.tst
index 5a5f0a5..22b46e4 100644
--- a/tst/bugfix.tst
+++ b/tst/bugfix.tst
@@ -497,5 +497,20 @@ true
 gap> Random( TrivialGroup( IsPcpGroup ) );
 id
 
+#
+# Fix a bug in IsNormal
+# <https://github.com/gap-packages/polycyclic/issues/46>
+#
+gap> g := PcGroupToPcpGroup(SmallGroup(48,1));
+Pcp-group with orders [ 2, 2, 2, 2, 3 ]
+gap> S := SylowSubgroup( g, 2 );
+Pcp-group with orders [ 2, 2, 2, 2 ]
+gap> T := S^g.5;
+Pcp-group with orders [ 2, 2, 2, 2 ]
+gap> IsNormal( S, T );
+false
+gap> IsNormal( T, S );
+false
+
 #
 gap> STOP_TEST( "bugfix.tst", 10000000);